arXiv subjects

Steve Campbell

Publications and source records attributed to Steve Campbell.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multiparameter critical quantum metrology with impurity probes

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin-1/2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo (2IK) model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular -- even though the parameters to be estimated are independent -- resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.

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arXiv2024

Universally Robust Quantum Control

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses which are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. We highlight the power of our results for error resistant single- and two-qubit gates.

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arXiv2024

Fisher information rates in sequentially measured quantum systems

We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the transitions between the measurement basis states that plays the most significant role in determining the precision, with the resulting conditional Fisher information being interpretable as a rate of information acquisition. Projective measurements are shown to elegantly demonstrate this in two disparate estimation settings. Firstly, in determining the temperature of an environment and, secondly, to ascertain a parameter of the system Hamiltonian. In both settings we show that the sequential estimation approach can provide a useful method to enhance the achievable precision.

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arXiv2023

Quantum work statistics of controlled evolutions

We use the quantum work statistics to characterize the controlled dynamics governed by a counterdiabatic driving field. Focusing on the Shannon entropy of the work probability distribution, $P(W)$, we demonstrate that the thermodynamics of a controlled evolution serves as an insightful tool for studying the non-equilibrium dynamics of complex quantum systems. In particular, we show that the entropy of $P(W)$ recovers the expected scaling according to the Kibble-Zurek mechanism for the Landau-Zener model. Furthermore, we propose that the entropy of the work distribution provides a useful summary statistic for characterizing the need and complexity of the control fields for many-body systems.

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arXiv2023

Robustness of controlled Hamiltonian approaches to unitary quantum gates

We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyse their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to time-keeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations.

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arXiv2023

DQC1 as an Open Quantum System

The DQC1 complexity class, or power of one qubit model, is examined as an open quantum system. We study the dynamics of a register of qubits carrying out a DQC1 algorithm and show that, for any algorithm in the complexity class, the evolution of the logical qubit can be described as an open quantum system undergoing a dynamics which is unital. Unital quantum channels respect the Tasaki-Crooks fluctuation theorem and we demonstrate how this is captured by the thermodynamics of the logical qubit. As an application, we investigate the equilibrium and non-equilibrium thermodynamics of the DQC1 trace estimation algorithm. We show that different computational inputs, i.e. different traces being estimated, lead to different energetic exchanges across the register of qubits and that the temperature of the logical qubit impacts the magnitude of fluctuations experienced and quality of the algorithm.

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arXiv2023

Entropy of the quantum work distribution

The statistics of work done on a quantum system can be quantified by the two-point measurement scheme. We show how the Shannon entropy of the work distribution admits a general upper bound depending on the initial diagonal entropy, and a purely quantum term associated to the relative entropy of coherence. We demonstrate that this approach captures strong signatures of the underlying physics in a diverse range of settings. In particular, we carry out a detailed study of the Aubry-André-Harper model and show that the entropy of the work distribution conveys very clearly the physics of the localization transition, which is not apparent from the statistical moments.

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arXiv2023

Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes

We study quantum impurity models as a platform for quantum thermometry. A single quantum spin-1/2 impurity is coupled to an explicit, structured, fermionic thermal environment which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.

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arXiv2023

Non-Gaussian work statistics at finite-time driving

We study properties of the work distribution of a many-body system driven through a quantum phase transition in finite time. We focus on the non-Gaussianity of the distribution, which we characterize through two quantitative metrics: skewness and negentropy. In particular, we focus on the quantum Ising model and show that a finite duration of the ramp enhances the non-Gaussianity of the distribution for a finite size system. By examining the characteristics of the full distribution, we observe that there is a clear intermediate regime between the sudden quench and adiabatic limits, where the distribution becomes increasingly skewed.

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arXiv2022

Optimal Control in Disordered Quantum Systems

We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this, we then show how this approach can be effectively adapted to control a disordered quantum system. We consider two settings: optimal control for a known unwanted disorder pattern, i.e. a specific disorder realisation, and optimal control where only the statistical properties of disorder are known, i.e. optimizing for high average fidelities. In the former, disorder effects can be effectively mitigated for an appropriately chosen control protocol. However, in the latter setting the average fidelity can only be marginally improved, suggesting the presence of a fundamental lower bound.

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arXiv2022

Minimal action control method in quantum critical models

We present a general protocol to control closed quantum systems that is based on minimising the adiabatic action. Using tools based on the geometry of quantum evolutions through the quantum adiabatic brachistochrone, we show that high fidelity control of the ground state of critical quantum systems can be achieved and requires only a reasonable approximation for the ground state spectral gap. We demonstrate our results for three widely applicable systems: the Landau-Zener, Ising, and fully connected spin models.

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arXiv2022

Periodically refreshed quantum thermal machines

We introduce unique class of cyclic quantum thermal machines (QTMs) which can maximize their performance at the finite value of cycle duration $τ$ where they are most irreversible. These QTMs are based on single-stroke thermodynamic cycles realized by the non-equilibrium steady state (NESS) of the so-called Periodically Refreshed Baths (PReB) process. We find that such QTMs can interpolate between standard collisional QTMs, which consider repeated interactions with single-site environments, and autonomous QTMs operated by simultaneous coupling to multiple macroscopic baths. We discuss the physical realization of such processes and show that their implementation requires a finite number of copies of the baths. Interestingly, maximizing performance by operating in the most irreversible point as a function of $τ$ comes at the cost of increasing the complexity of realizing such a regime, the latter quantified by the increase in the number of copies of baths required. We demonstrate this physics considering a simple example. We also introduce an elegant description of the PReB process for Gaussian systems in terms of a discrete-time Lyapunov equation. Further, our analysis also reveals interesting connections with Zeno and anti-Zeno effects.

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arXiv2022

Commutativity and the emergence of classical objectivity

We examine how the ability of a system to redundantly proliferate relevant information about its pointer states is affected when it is coupled to multiple baths. To this end, we consider a system in contact with two baths: one -- termed the {\it accessible} environment -- which, on its own, induces a pure dephasing mechanism on the state of the system and satisfies the conditions for classical objectivity to be established. The second environment, which we dub as {\it inaccessible}, affects the system in two physically relevant ways. Firstly, we consider an interaction that commutes with the Hamiltonian describing the interaction between system and accessible bath. It thus also gives rise to dephasing of the system, albeit on different time scales. Secondly, we consider a thermalising interaction, which does not commute with the system-accessible environment Hamiltonian. While the former still allows the system to redundantly encode its state into the accessible environment, the latter degrades the correlations, eventually destroying them in the long-time limit, and thus leads to a loss of the conditions necessary for classical objectivity to be established. This sheds light on the role that commutativity between the various system-bath interaction terms plays when establishing the conditions for classical objectivity to be supported.

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arXiv2022

Classical dissipative cost of quantum control

Protocols for non-adiabatic quantum control often require the use of classical time varying fields. Assessing the thermodynamic cost of such protocols, however, is far from trivial. In this letter we study the irreversible entropy produced by the classical apparatus generating the control fields, thus providing a direct link between the cost of a control protocol and dissipation. We focus, in particular, on the case of time-dependent magnetic fields and shortcuts to adiabaticity. Our results are showcased with two experimentally realisable case studies: the Landau-Zener model of a spin-1/2 particle in a magnetic field and an ion confined in a Penning trap.

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arXiv2022

Correlations, information backflow, and objectivity in a class of pure dephasing models

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a class of dephasing models where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen-Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some will exhibit quantum Darwinistic features, while others show no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system's ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity.

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arXiv2022

Counterdiabatic control in the impulse regime

Coherent control of complex many-body systems is critical to the development of useful quantum devices. Fast perfect state transfer can be exactly achieved through additional counterdiabatic fields. We show that the additional energetic overhead associated with implementing counterdiabatic driving can be reduced while still maintaining high target state fidelities. This is achieved by implementing control fields only during the impulse regime, as identified by the Kibble-Zurek mechanism. We demonstrate that this strategy successfully suppresses most of the defects that would be generated due to the finite driving time for two paradigmatic settings: the Landau-Zener model and the Ising model. For the latter case, we also investigate the performance of our impulse control scheme when restricted to more experimentally realistic local control fields.

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arXiv2022

Diverging quantum speed limits: a herald of classicality

When is the quantum speed limit (QSL) really quantum? While vanishing QSL times often indicate emergent classical behavior, it is still not entirely understood what precise aspects of classicality are at the origin of this dynamical feature. Here, we show that vanishing QSL times (or, equivalently, diverging quantum speeds) can be traced back to reduced uncertainty in quantum observables and thus can be understood as a consequence of emerging classicality for these particular observables. We illustrate this mechanism by developing a QSL formalism for continuous variable quantum systems undergoing general Gaussian dynamics. For these systems, we show that three typical scenarios leading to vanishing QSL times, namely large squeezing, small effective Planck's constant, and large particle number, can be fundamentally connected to each other. In contrast, by studying the dynamics of open quantum systems and mixed states, we show that the classicality that emerges due to incoherent mixing of states from the addition of classical noise typically increases the QSL time.

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arXiv2021

Stochastic collisional quantum thermometry

We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model.

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